The Illinois Republican Party characterized Jones as a Nazi and publicly denounced him in both the 2018 and 2020 races for Illinois' 3rd Congressional District. In 2020, the party ran an ad campaign against Jones that included a digital ad titled, "Say No To The Nazi." According to The New York Times, Jones is a former member of the American Nazi Party. Illinois Republican Party chairman Tim Schneider said of Jones in 2020, “Arthur Jones isn’t a Republican, and we’re going to expose people to who he really is and do everything we can to educate Republicans not to vote for Arthur Jones...we’re going to do everything we can to distance ourselves from this Neo-Nazi who is running as a Republican.” In a news release endorsing Jones' opponent Mike Fricilone in the 2020 Republican primary, Republican state senate leader Bill Brady called Jones a "fake Republican."

Jones received criticism when an article came out in the Oak Lawn Patch on February 29, 2012, in which he commented that "the Holocaust is nothing more than an international extortion racket by the Jews. It's the blackest lie in history." According to the same article, Jones participated in the Nazis' 1978 march in Chicago and "neither denies nor repudiates" having had been affiliated with the neo-Nazi Party, although he said he votes Republican "90 percent of the time." Jones' 2016 campaign website contained a section called "Holocaust?" featuring write-ups and newspaper clippings supporting his belief that the Holocaust is "mythical." Jones cited tax benefits received by Holocaust survivors as a possible motivation for their upholding of the narrative. He also claimed on the website that Kosher food labels are "another Jewish racket, pure and simple to extort money out of the food manufacturers at a hefty fee, which is then passed on to all non-Jewish customers in the retail price paid each time we shop." In the past, Jones participated in public debates about the Holocaust at Naperville Central High School, arguing against Robert Leroi.